12.2: Inductively Strong Arguments

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When things are uncertain in these ways, we usually cannot expect to find deductively valid arguments. At most we can hope to find arguments that are inductively strong. In an earlier chapter, we saw that an argument is inductively strong just in case:

If all its premises are true, then there is a high probability that its conclusion will be true as well.
It is not deductively valid.

The first item is the important one (the point of the second item is to ensure that no argument is both deductively valid and inductively strong; this makes things easier for us in various ways).

There are two important ways in which inductive strength differs from deductive validity:

Unlike deductive validity, inductive strength comes in degrees.
In a deductively valid argument, the conclusion does not contain any information that was not already present in the premises. By contrast, in an inductively strong argument, the conclusion contains new information.

Since the conclusion contains new information, we go beyond the information that is stated in our premises. Inductively strong arguments and reasons can take many different forms; in this module, we will focus on those that involve probability.

We can also speak of inductively strong reasons. A group of sentences provide inductive reasons for a conclusion just in case it is unlikely for all of them to be true and the conclusion false. There is always an inductive leap from the inductively strong reasons to the conclusion. The stronger the inductive reasons, the less risky the inductive leap.

Kinds of Reasoning

We can make a sharp distinction between deductively valid arguments, on the one hand, and those that are merely inductively strong, on the other, and it is important to be clear about the difference. But in everyday life there is often no very clear distinction between deductive and inductive reasoning. What might seem to be invalid might become valid if we supply plausible missing premises, for example. Still, a great deal of our reasoning involves arguments and evidence that are inductively uncertain. Life is full of risks and uncertainty, and so is our reasoning about it. No methods are foolproof, but some are much better than others.